Non-linear MHD modelling of shattered pellet injection in ASDEX Upgrade

Shattered pellet injection (SPI) is selected for the disruption mitigation system in ITER, due to deeper penetration, expected assimilation efficiency and prompt material delivery. This article describes non-linear magnetohydrodynamic (MHD) simulations of SPI in the ASDEX Upgrade tokamak to test the mitigation efficiency of different injection parameters for neon-doped deuterium pellets using the JOREK code. The simulations are executed as fluid simulations, while additional marker particles are used to evolve the charge state distribution and radiation property of impurities based on OpenADAS atomic data, i.e., a collisional-radiative model is used. Neon fraction scans between 0 - 10% are performed. Numerical results show that the thermal quench (TQ) occurs in two stages. In the first stage, approximately half of the thermal energy is abruptly lost, primarily through convective and conductive transport in the stochastic fields. This stage is relatively independent of the neon fraction. In the second stage, where the majority of the remaining thermal energy is lost, radiation plays a dominant role. In case of pure deuterium injection, this second stage may not occur at all. A larger fraction ($\sim $20%) of the total material in the pellet is assimilated in the plasma for low neon fraction pellets ($\leq 0.12%$) due to the full thermal collapse of the plasma occurring later than in high neon fraction scenarios. Nevertheless, the total number of assimilated neon atoms increases with increasing neon fraction. The effects of fragment size and penetration speed are then numerically studied, showing that slower and smaller fragments promote edge cooling and the formation of a cold front. Faster fragments result in shorter TQ duration and higher assimilation as they reach the hotter plasma regions quicker.

💡 Research Summary

This paper presents a comprehensive three‑dimensional non‑linear magnetohydrodynamic (MHD) study of shattered pellet injection (SPI) in the ASDEX Upgrade (AUG) tokamak, with the aim of informing the design of ITER’s disruption mitigation system (DMS). The authors employ the JOREK code, which solves a visco‑resistive reduced MHD model with separate ion and electron temperature equations, to simulate the full thermal quench (TQ) and early current quench (CQ) phases following the injection of neon‑doped deuterium pellets. In addition to the fluid description, a set of marker particles is introduced to carry the impurity charge‑state distribution; these markers evolve according to OpenADAS atomic data, providing a self‑consistent collisional‑radiative model for radiation and ionization power losses.

A series of parameter scans is performed. Neon fractions in the pellet are varied from 0 % to 10 % (0, 0.12, 1, and 10 % by atom number). Three fragment‑size regimes are generated by changing the shatter angle (12.5°, 20°, 25°), which yields 53 (large‑fragment, LF), 199 (medium‑fragment, MF), and 1105 (small‑fragment, SF) fragments per pellet. For each size case, two injection‑speed scenarios are examined: the nominal pre‑shattered speed of 443 m s⁻¹ (full velocity, FV) and a reduced speed of 222 m s⁻¹ (half velocity, HV). The fragment radius distribution follows Parks’ fragmentation model, while velocities are sampled from a Gaussian distribution centred on the mean of the parallel and pellet speeds, with a 20 % standard deviation. The initial fragment cloud originates at the midpoint of the shatter tube and is directed toward the plasma core.

The equilibrium used for all simulations is an AUG H‑mode discharge (#40355) reconstructed with CLISTE, featuring a toroidal field of 1.8 T, plasma current of 0.8 MA, edge electron temperature ≈6 keV, and a safety‑factor profile typical of high‑performance scenarios. The computational mesh is flux‑aligned, contains an X‑point, and has a resolution of 70 radial by 110 poloidal points; eight toroidal harmonics (n = 0…7) are retained. Physical diffusivities are set to realistic values (η follows a Spitzer‑like T⁻³ᐟ² law with cut‑offs at 1 eV and 1.35 keV, μ = 4.85 × 10⁻⁷ kg m⁻¹ s⁻¹, χ⊥ = 1 m² s⁻¹, χ∥ = 3.6 × 10²⁹ Tₑ⁵ᐟ² nₑ⁻¹ m² s⁻¹). A time step of 6.1 × 10⁻⁸ s is used during the CQ, with adaptive increase later. No background impurities or initial magnetic perturbations are included, allowing the focus to remain on the injected material.

The simulations reveal a robust two‑stage TQ dynamics that is largely independent of the neon fraction in the first stage. In stage 1, roughly half of the total thermal energy is lost abruptly through convective and conductive transport driven by stochastic magnetic fields generated as the fragments penetrate the edge plasma. This loss occurs on a sub‑millisecond timescale and is dominated by the rapid ablation of fragments in the outer region; the neon content does not significantly affect the magnitude or timing of this stage.

Stage 2 commences once the plasma temperature has dropped sufficiently for radiation to become the dominant energy sink. In cases with any neon present, the impurity radiation rises sharply, accounting for up to 30–40 % of the total energy loss and extending the TQ duration. For pure deuterium injection, the radiative phase is essentially absent, leading to a shorter overall TQ and a lower total energy loss. The transition between the two stages is marked by a rapid increase in the OpenADAS‑computed radiated power (P_rad) and a corresponding rise in the ionization power (P_ion) as neon charge states evolve from low‑Z to higher‑Z configurations.

Material assimilation shows a nuanced dependence on neon fraction. Low‑neon pellets (≤0.12 % neon) achieve a higher overall assimilation fraction of the injected mass—about 20 % of the total pellet material is incorporated into the plasma. This is because the slower radiative cooling allows the fragments to penetrate deeper before being fully ablated, leading to a more complete thermal collapse. As the neon fraction increases, the total assimilated mass fraction declines, but the absolute number of assimilated neon atoms rises roughly linearly with the neon content. Consequently, the radiative efficiency (radiated energy per neon atom) improves with higher neon doping, even though the overall pellet assimilation drops.

Fragment size and injection speed exert a strong influence on both the TQ timescale and assimilation. Small‑fragment (SF) cases produce a broad, cold front at the plasma edge, promoting strong edge cooling and a prolonged TQ. The cold front propagates inward, generating a “cold‑front” structure that delays the onset of the radiative stage. Conversely, large‑fragment (LF) cases reach the hot core more quickly, shortening the TQ (often <0.8 ms) and increasing the assimilation fraction. Faster fragments (FV) similarly reduce the TQ duration and enhance assimilation because they experience less ablation in the periphery and deliver material deeper into the plasma. The half‑velocity (HV) scenarios demonstrate that reducing the parallel component of the fragment velocity while keeping the perpendicular component constant leads to a noticeable lengthening of the TQ and a reduction in the total assimilated neon, confirming the importance of penetration speed for effective mitigation.

The authors also discuss numerical considerations. To avoid unphysical resistivity blow‑up at very low temperatures, a floor of 1 eV is imposed, and a ceiling of 1.35 keV limits the resistivity at high temperature. The parallel viscosity and thermal conductivity are set to realistic Spitzer values, and particle diffusivities for both bulk ions and impurities are taken as 1.6 m² s⁻¹. Convergence tests on the number of toroidal modes confirm that eight harmonics capture the essential 3‑D dynamics without excessive computational cost.

In summary, this work provides the first large‑scale 3‑D JOREK simulations that couple fluid MHD with a self‑consistent collisional‑radiative impurity model for SPI in a realistic AUG configuration. The key findings are: (1) TQ proceeds in two distinct phases—initial stochastic transport‑dominated loss followed by radiation‑dominated loss; (2) neon doping controls the radiative phase but does not affect the early stochastic loss; (3) low neon fractions maximize total material assimilation, while higher neon fractions maximize radiated power per atom; (4) larger fragments and higher injection speeds improve deep penetration, shorten TQ, and increase assimilation; (5) slower, smaller fragments enhance edge cooling and produce a cold front that prolongs the TQ. These insights directly inform the selection of fragment size, shatter angle, injection speed, and neon concentration for ITER’s SPI‑based disruption mitigation system, balancing the need for rapid thermal energy removal, adequate material assimilation, and effective runaway electron suppression.